Multigrid methods for a parameter dependent problem in primal variables

:in this paper we consider multigrid methods for the parameter dependent pr oblem of nearly incompressible materials. We construct and analyze multilev el-projection algorithms, which can be applied to the mixed as well as to t he equivalent, non-conforming finite element: scheme in primal variables. F or proper norms, we prove that the smoothing property: and the approximatio n property hold with constants that are independent of the small parameter, Thus we obtain robust and optimal convergence rates for the Wcycle and the variable V-cycle multigrid methods. The numerical. results pretty well con form the robustness and optimality of the multigrid methods proposed. Mathe matics Subject Classification (1991): 65N55.